A critical part of clinical trials in drug development is the analysis of treatment efficacy in patient subgroups (subpopulations). Due to multiplicity and the small sample sizes involved, this analysis presents substantial statistical challenges and can lead to misleading conclusions. In this thesis, we develop methodology for statistically valid subgroup analysis in a variety of settings. First, we consider a number of trial designs of varying flexibility for the case of one subgroup of interest. Some procedures are novel, while others are adapted from the literature. Included is data-driven consideration of adaptive change of subject eligibility criteria-known as adaptive enrichment-whereby apparently nonresponsive patient populations are not recruited after data has been unblinded for an interim analysis. We conduct an extensive numerical study to investigate design operating characteristics, as well as sensitivity to subgroup prevalence and interim analysis timing. We observe that power gains can be substantial when a treatment is only effective in the subgroup of interest. Following this example, selected procedures are generalized to allow for analysis of an arbitrary number of subgroups. Next, we propose a K -stage group sequential design that can be applied as a confirmatory seamless Phase II/III design. The design is specified through upper and lower spending functions, defined in terms of calendar times. After the first stage, poorly performing subgroups are eliminated and the remaining population is pooled for the duration of the trial. This procedure combines the elimination of non-sensitive subgroups with the definitive assessment of treatment efficacy associated with traditional group sequential designs. Numerical examples show that the procedure has high power to detect subgroup-specific effects, and the use of multiple interim analysis points can lead to substantial sample size savings. We address the challenges of adjusting for selection bias, and protecting the familywise error rate in the strong sense. All designs are presented either in terms of standardized test statistics or the efficient score, making the analysis of normal, binary, or time-to-event data straightforward.